How effective is advertising in duopoly markets?

A simple Ising spin model which can describe the mechanism of advertising in a duopoly market is proposed. In contrast to other agent- based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among customers. It is shown via standard Monte Carlo simulations that very simple rules and inclusion of an external field - an advertising campaign - lead to phase transitions, ie. extreme and fast changes in market share.advertising, oligopoly, duopoly, Ising model, agent-based model

Evolution in a changing environment

We propose a simple model, based on Monte Carlo simulations, for studying the effects of changes in the environment on the adaptation and extinction of evolving species. We show that the geological data of climatic changes are well described by Levy-stable distributions. This leads, in our model, to a fairly good reproduction of the known data on species extinctions. We have also found that the dependence of the probability that a given number of species becomes extinct in one time step, on the number of extinct species shows a cross-over from an exponential to a power-like character.Levy-stable distribution; Monte Carlo simulation; Species extinction; Evolution;

Measuring Anti-Correlations in the Nordic Electricity Spot Market by Wavelets

We consider the Nordic electricity spot market from mid 1992 to the end of year 2000. This market is found to be well approximated by an anti-persistent self-affine (mean-reverting) walk. It is characterized by a Hurst exponent of $H\simeq 0.41$ over three orders of magnitude in time ranging from days to years. We argue that in order to see such a good scaling behavior, and to locate cross-overs, it is crucial that an analyzing technique is used that {\em decouples} scales. This is in our case achieved by utilizing a (multi-scale) wavelet approach. The shortcomings of methods that do not decouple scales are illustrated by applying, to the same dat a set, the classic $R/S$- and Fourier techniques, for which scaling regimes and/or positions of cross-overs are hard to define.Comment: Latex, 11 pages including 4 figures. To appear Physica

Heavy-tails and regime-switching in electricity prices

In this paper we first analyze the stylized facts of electricity prices, in particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of price changes. Then we calibrate Markov regime-switching (MRS) models with heavy-tailed components and show that they adequately address the aforementioned characteristics. Contrary to the common belief that electricity price models ‘should be built on log-prices’, we find evidence that modeling the prices themselves is more beneficial and methodologically sound, at least in case of MRS models.Electricity spot price, Heavy-tails, Spikes, Markov regime-switching, Pareto distribution

Modeling electricity loads in California: a continuous-time approach

In this paper we address the issue of modeling electricity loads and prices with diffusion processes. More specifically, we study models which belong to the class of generalized Ornstein-Uhlenbeck processes. After comparing properties of simulated paths with those of deseasonalized data from the California power market and performing out-of-sample forecasts we conclude that, despite certain advantages, the analyzed continuous-time processes are not adequate models of electricity load and price dynamics.Comment: To be published in Physica A (2001): Proceedings of the NATO ARW on Application of Physics in Economic Modelling, Prague, Feb. 8-10, 200

Heavy tails and electricity prices

In the first years after the emergence of deregulated power markets it became apparent that for the valuation of electricity derivatives we cannot simply rely on models developed for financial or other commodity markets. However, before adequate models can be put forward the unique characteristics of electricity (spot) prices have to be thoroughly analyzed. In particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of returns. In this paper we first analyze the stylized facts of electricity prices, then present two modeling approaches: jump-diffusion and regime-switching, which to some extent address the pertinent issues.Heavy-tailed distribution; Electricity spot price; Seasonality; Volatility; Price spike;

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable (alpha- stable) distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0Levy-stable distribution, Alpha-stable distribution, Tail exponent, Hill estimator